1. Field of the Invention
The present invention relates to a muffler for automobiles, and more particularly, an improvement of such a muffler with regard to the muffling performance thereof.
2. Description of the Prior Art
The exhaust system for an automobile engine incorporates therein a muffler for reducing the engine exhaust noise. As a type of the mufflers for this purpose, there is known a muffler which comprises an expansion chamber of a substantially drum-like shape having an equivalent diameter D and a length h, gas inlet and outlet pipes connected to said expansion chamber so as to cause a gas flow which traverses said expansion chamber substantially diametrically therethrough, and a low frequency resonator chamber axially connected to said expansion chamber, wherein said drum-shaped expansion chamber has a circular elliptical or a similar sectional shape. In the muffler of this type, the exhaust gas flow is applied expansion and contraction while it flows from the gas inlet pipe to the gas outlet pipe by traversing the expansion chamber substantially diametrically therethrough, thereby effecting a reduction of high to medium frequency noises, while on the other hand a low frequency noise included in the gas flow is reduced by the resonance effect applied by the resonator chamber.
The lower frequency resonator chamber is generally the Helmholtz resonator, which comprises a closed chamber and an insert pipe and is generally effective for reducing a low frequency noise having a frequency of 60-150 Hz which causes a humming noise in the passenger compartment. The resonant frequency of the Helmholtz resonator is given by the following well known formula: EQU f.sub.r = (C/2.pi.) .sqroot.(Co/V) (1)
wherein
f.sub.r = resonant frequency PA1 C = sound velocity PA1 V = volume of the resonator chamber PA1 Co = propagation constant PA1 a = radius of the insert pipe PA1 l = length of the insert pipe PA1 .beta. = constant such as (.pi./2) .about. (.pi./4) PA1 h = length of the expansion chamber
Co is given by the following formula: EQU Co = .pi.a.sup.2 /(l + .beta.a) (2)
wherein
Since the low frequency resonator chamber effects reduction of noise by resonance, a good silencing effect is obtained when the velocity of the exhaust gas flow traversing the inlet portion of the insert pipe is judiciously designed in view of the resonance frequency of the resonator chamber while the impedance of the expansion chamber is designed to be sufficiently high relative to that of the resonator chamber. For the muffler of the abovementioned structure, the noise pressure reduction obtained by the low frequency resonator chamber is determined by the following formula: ##EQU1## wherein Att = noise pressure reduction
Since the volume of the resonator chamber (V), the radius (a) and the propagation constant (Co) are determined in relation to the design resonant frequency of the low frequency resonator chamber, it is more desirable that the length (h) of the expansion chamber is smaller for obtaining a larger noise pressure reduction Att for a better silencing effect. In other words, when the length h of the expansion chamber is made smaller, the impedance of the expansion chamber is increased so that the resonance effected by the low frequency resonator chamber is more activated thereby increasing the silencing effect.
However, when the length h of the expansion chamber is reduced, the back pressure for the engine increases, whereby there occurs various problems such as the reduction of the engine output power, the generation of the gas flow noise, the increase of a high frequency noise, etc.